Team:Dundee/Modeling/Appendix2

Dry Lab


Appendix 2: Fingerprint Ageing Code

Principal Component Analysis Code

Squalene Epoxide Model Code

Principal Component Analysis Code


Principal component analysis was performed using MATLAB software to produce the data and figures described in the PCA Section. The MATLAB file can be seen below, where green represents comments to aid in understanding the commands.



MATLAB code from FrickPCA.m file
%% Section 1. Importing the data from excel onto MATLAB.
filename = 'frick.xlsx';
sheet = 3; % Sheet 3 contains only normalised values with all donors encapsulated into a single matrix.
xlrange = 'B2:JN16';
A = xlsread(filename,sheet,xlrange);
% Raw chromatogram values have been normalized to the sum to take measure the quantitative changes between the different compounds analysed in the dataset.
%
%
%% Section 2. Normalisation and Orthogonal transformation of data.
data = A; [M,N] = size(data); mn = mean(data,2);
dataN = data - repmat(mn,1,N) ; %data normalising by subtracting column mean from each column.
Z= dataN' / sqrt(N-1);
[u,S,PC] = svd(Z); %Singular value decomposition
signals = PC'*dataN;
% In order to have total control and understanding of the matrix operations behind the PCA, the traditional singular value decomposition linear algebraic operations were used instead of the PCA MATLAB function on the data.
%
%
%% Section 3. Scoreplot of Interdonal variation with respect to first two PCs.
pointsize=50;
figure % Scoreplot of Interdonal variation
colour1= [ [0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0];[0.5 0.5 0]; [0.5 0.5 0];[0.5 0.5 0];[1 0 1]; [1 0 1];[1 0 1];[0 0.5 0.5]; [0 0.5 0.5];[0 0.5 0.5];[0.5 0 0];[0.5 0 0];[0.5 0 0]; [0 0.5 0];[0 0.5 0];[0 0.5 0]; [0 0 0.4]; [0 0 0.4];[0 0 0.4];[1 0 0];[1 0 0];[1 0 0]];
scatter(signals(1,:),signals(2,:),pointsize,colour1,'filled');
title('Scoreplot Of Interdonal Variation In Fingerprints Against Time W.R.T First Two Principal Components')
xlabel('PC1')
ylabel('PC2')
text(-0.5,-0.201,'\bf \fontsize{10}Donor Key'); %Artisan Legend
text(-0.5,-0.234,'\bf \color[rgb]{0.5,0.5,0}{\fontsize{14}{\bullet}}  \color[rgb]{0,0,0} \fontsize{10}CB003');
text(-0.5,-0.256,'\bf \color[rgb]{1,0,1}{\fontsize{14}{\bullet}}  \color[rgb]{0,0,0} \fontsize{10}CA006');
text(-0.5,-0.278,'\bf \color[rgb]{0,0.5,0.5}{\fontsize{14}{\bullet}}  \color[rgb]{0,0,0} \fontsize{10}CB033');
text(-0.5,-0.3,'\bf \color[rgb]{0.5,0,0}{\fontsize{14}{\bullet}}  \color[rgb]{0,0,0} \fontsize{10}DA080');
text(-0.5,-0.322,'\bf \color[rgb]{0,0.5,0}{\fontsize{14}{\bullet}}  \color[rgb]{0,0,0} \fontsize{10}CA100');
text(-0.5,-0.344,'\bf \color[rgb]{0,0,0.4}{\fontsize{14}{\bullet}}  \color[rgb]{0,0,0} \fontsize{10}DA103');
text(-0.5,-0.366,'\bf \color[rgb]{1,0,0}{\fontsize{14}{\bullet}}  \color[rgb]{0,0,0} \fontsize{10}CB135');
%This figure shows interdonal variation between all the donors and their aged fingerprint samples from all ageing intervals. Along the first PC, both inter and intra variation appear to increase. Moreover, this graph shows that individual donor samples DO NOT distinctly group together in a dichotomous manner which means that it would not be possible to deduce which fingerprint corresponds to which donor based on their Principal Components (PCs). The donor dots appear to follow faintly separate trajectories along the first PC axis, this suggests a distinct intradonal variation across all donors. This partly confirms the feasibility of a fingerprint age presumptive test. To further understand the nature of fingerprint compound degradation and its relationship between donors the following must be investigated: How much of which compounds contribute to forming the first two principal components?
%This would be explored through 'factor loading'(See Section 14 of code), How much do the first two PCs represent the total variance of the dataset?(See Section 7 of code), and if fingerprints from different donors age the at the same rate? (Section 4)
%
%
%% Section 4. Scoreplot of composite degradation against time with respect to first two PCs.
figure
colour2=[ [1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];[1 1 0];...
    [0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];[0 0 0.2];...
    [0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0]; [0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];[0 0.3 0];...
    [0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3]; [0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];[0 0.3 0.3];...
    [0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];[0.4 0 0.4];...
    [0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];[0.2 0 0];...
    [0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];[0.1 0.1 0];...
    [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6]; [0 0 0.6];[0 0 0.6];...
    [0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];[0 0.9 0];...
    [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6]; [0 0.6 0.6];[0 0.6 0.6];...
    [0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];[0.8 0 0.8];...
    [0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];[0.8 0 0];...
    [0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0];[0.5 0.5 0]];
scatter(signals(1,:),signals(2,:),pointsize,colour2,'filled');
title('Scoreplot of Composite Degradation Against Time W.R.T The First Two Principal Components');
xlabel('PC1');
ylabel('PC2');
text(0.62,0.2,'Time (days)');
text(0.62,0.15,'\bf\color[rgb]{1,1,0}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 0');
text(0.62,0.125,'\bf\color[rgb]{0,0,0.2}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 2');
text(0.62,0.1,'\bf\color[rgb]{0,0.3,0}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 5');
text(0.62,0.075,'\bf\color[rgb]{0,0.3,0.3}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 7');
text(0.62,0.05,'\bf\color[rgb]{0.4,0,0.4}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 9');
text(0.62,0.025,'\bf\color[rgb]{0.2,0,0}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 12');
text(0.62,0,'\bf\color[rgb]{0.1,0.1,0}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 14');
text(0.62,-0.025,'\bf\color[rgb]{0,0,0.6}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 16');
text(0.62,-0.05,'\bf\color[rgb]{0,0.9,0}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 19');
text(0.62,-0.075,'\bf\color[rgb]{0,0.6,0.6}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 21');
text(0.62,-0.1,'\bf\color[rgb]{0.8,0,0.8}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 23');
text(0.62,-0.125,'\bf\color[rgb]{0.8,0,0}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 26');
text(0.62,-0.15,'\bf\color[rgb]{0.5,0.5,0}{\fontsize{14}{\bullet}} \color{black}\fontsize{10}Day 28');
%This PC graph with respect to time is difficult to interpret due to the plethora of colours. The graph shows that the older a fingerprint is the more difficult it is to pinpoint their age. The lack of distinct groupings between tandem day intervals shows that fingerprints do not age at a constant rate across all donors. This suggests that to construct an age curve would require intra specificity. This rejects the hypothesis of creating a 'one size fits all age curve' for any random fingerprnt of age deduction. An attempt to explore the behaviour of aged fingerprints in greater detail is in section 17.
%
%
%% Section 5. Scatterplot of entire signal data in 3D.
figure
scatter3(signals(1,:),signals(2,:),signals(3,:),pointsize,colour1,'filled')
title('Interdonal Variation Represented By First Three Principal Components')
xlabel('PC1')
ylabel('PC2')
zlabel('PC3')
correctedPosition = get(gcf,'Position') + [21 -125 0 0];
fps = 60; sec = 5;

vidObj = VideoWriter('newfile.avi');
vidObj.Quality = 100;
vidObj.FrameRate = fps;

open(vidObj);
for i=1:fps*sec
  camorbit(0.9,-0.1);
  writeVideo(vidObj,getframe(gcf, correctedPosition));
end
close(vidObj);
% Video animation of Interdonal variation along first three PCs.
%
%
%% Section 6. Comparing eigenvalues from PCA and SVD.
[COEFF,SCORE,latent]=pca(data'); % Transpose data before plugging into function
% PCA function was applied to the normalised data to compare the eigenvalues from the covariance matrix diag(S) with latent.
latent; % Returns the eigenvalues of the covariance matrix.
% latent omits zero value eigenvalues.
eigenSVD = diag(S).^2;
%Both methods of analysis are expected to provide different principal components but the same eigenvalues. This is a check for consistency.
%
%

%% Section 7. Evaluation of variance coverage by principal components.
latentcov=cumsum(latent)./sum(latent);   % 98% of the variance is accounted for by first 3 PCs from PCA package.
Scoverage=cumsum(diag(S))./sum(diag(S)); % 76% of the var is accounted for by the first 3 PCs from svd package.
%
%
%% Section 8. Curating normalised data for CB003 donor.
CB003_dataN = array2table(dataN);
filename2 = 'CB003Norm.xlsx';
writetable(CB003_dataN,filename2,'sheet',1); %Used this newly created spreadsheet on Excel to
%manually cut out CB003 from the rest of the donors
SheetCB3_2 = 2;
xlrange1= 'A1:AM15';
CB003 = xlsread(filename2,SheetCB3_2,xlrange1);
%
%
%% Section 9. Curating normalised data to for CB135 donor.
SheetCB135_3 = 3;
CB135 = xlsread(filename2,SheetCB135_3,xlrange1);
%
%
%% Section 10. CB003 interdonal PCA.
signalsCB003 = PC'*CB003;
figure
scatter(signalsCB003(1,:),signalsCB003(2,:),'filled')%first row all columns,second row all columns.
title('CB003 Interdonal Score Plot Analysis')
xlabel('PC1')
ylabel('PC2')
%This figure shows how much the principle components for the whole sample reflects on the particular CB003 donor in other words, the interdonor variation between CB003 and the rest of the samples.
%
%
%% Section 11. CB135 interdonal PCA.
signalsCB135 = PC'*CB135;
figure
scatter(signalsCB135(1,:),signalsCB135(2,:))
title('CB135 interdonal score plot analysis')
xlabel('PC1')
ylabel('PC2')
% Measuring the degradation of composites from donor CB135 against the PCs
% of entire sample.
%
%
%% Section 12. PCA Intravariation in CB003.
Z1 = CB003'/sqrt(N-1);
[u1,S1,PC1]= svd(Z1); % Principal matrix made only by CB003 sample alone
intrasignalCB3 = PC1'*CB003;
figure
scatter(intrasignalCB3(1,:),intrasignalCB3(2,:),'filled')
title('Intravariation scoreplot of first two principal components of Donor CB003')
xlabel('PC1')
ylabel('PC2')
%
%
%% Section 13. PCA Intravariation in CB135.
Z2 = CB135'/sqrt(N-1);
[u2,S2,PC2] = svd(Z2);
intrasignalCB135=PC2'*CB135;
figure
scatter(intrasignalCB135(1,:),intrasignalCB135(2,:))
title('Intravariation scoreplot of first two principal components of Donor CB135')
xlabel('PC1')
ylabel('PC2')
%
%
%% Section 14. Factor loadings for PC produced from SVD.
% This tells us how much each compound contributes to each of the primary three principal components given that PC1 accounts for 60% of the data according to the SVD reading on chapter 7.
signalT = signals';
figure
biplot(PC(:,1:2),'scores',signalT(:,1:2),'VarLabels',...
    {'Tetra','Penta','Hexa','Palmitic','Oliec','Stearic','Squalene','C24','C30:1','C30:0','CHO','C32:1','C32:0','C34:1','C34:0'},'LineWidth',2)
% (:,1:2) = all rows of first two columns--opposite to written algrebra
title('Biplot Of Finger Composite Contribution To First Two Principal Components [SVD]')
xlabel('PC1')
ylabel('PC2')
figure
biplot(PC(:,1:3),'scores',signalT(:,1:3),'VarLabels',...
    {'Tetra','Penta','Hexa','Palmitic','Oliec','Stearic','Squalene','C24','C30:1','C30:0','CHO','C32:1','C32:0','C34:1','C34:0'})
title('Biplot Of Finger Composite Contribution To First Three Principal Components [SVD]')
%
%
%% Section 15. Factor loadings for PC produced from PCA package.
figure
biplot(COEFF(:,1:2),'Scores',SCORE(:,1:2),'VarLabels',...
    {'Tetra','Penta','Hexa','Palmitic','Oliec','Stearic','Squalene','C24','C30:1','C30:0','CHO','C32:1','C32:0','C34:1','C34:0'})
title('Biplot Of Finger Composite Contribution To First Two Principal Components [PCA]')
xlabel('PC1')
ylabel('PC2')
figure
biplot(COEFF(:,1:3),'Scores',SCORE(:,1:3),'VarLabels',...
     {'Tetra','Penta','Hexa','Palmitic','Oliec','Stearic','Squalene','C24','C30:1','C30:0','CHO','C32:1','C32:0','C34:1','C34:0'})
 title('Biplot Of Finger Composite Contribution To First Three Principal Components [PCA]')
 xlabel('PC1')
 ylabel('PC2')
 zlabel('PC3')
 correctedPosition = get(gcf,'Position') + [21 -125 0 0];
fps = 60; sec = 10;

vidObj = VideoWriter('newfile.avi');
vidObj.Quality = 100;
vidObj.FrameRate = fps;

open(vidObj);
for i=1:fps*sec
  camorbit(0.9,-0.1);
  writeVideo(vidObj,getframe(gcf, correctedPosition));
end
close(vidObj);
%Results suggest Squalene consitutes 80% of the first PC and 20% of the second.
%Palmitic acid constitutes 65% of second PC and -40% of first.
%
%
%% Section 16. PC1 Axis Comparison.
%In order to view the relationship between time and squalene more clearly,the samples of each donor were grouped based on age and plotted against PC1 to see how the data aligns. This also aims to see whether or not squalene breaks down at a consistent rate across all donors.

% Day 0
Sheet_time_0 = 6;
xlranget0= 'B2:V16';
day_0 = xlsread(filename,Sheet_time_0,xlranget0);
[M1,N1] = size(day_0); mn1 = mean(day_0,2);
day0N = day_0 - repmat(mn,1,N1);
signals_t_0 = PC'*day0N;

% Day 2
Sheet_time_2 = 6;
xlranget2= 'B19:V33';
day_2 = xlsread(filename,Sheet_time_2,xlranget2);
mn2 = mean(day_2,2);
day2N = day_2 - repmat(mn2,1,N1);
signals_t_2 = PC'*day2N;

% Day 5
Sheet_time_5 = 6;
xlranget5= 'B36:V50';
day_5 = xlsread(filename,Sheet_time_5,xlranget5);
mn3 = mean(day_5,2);
day5N = day_5 - repmat(mn3,1,N1);
signals_t_5 = PC'*day5N;

% Day 7
Sheet_time_7 = 6;
xlranget7= 'B53:V67';
day_7 = xlsread(filename,Sheet_time_7,xlranget7);
mn4 = mean(day_7,2);
day7N = day_7 - repmat(mn4,1,N1);
signals_t_7 = PC'*day7N;

% Day 9
Sheet_time_9 = 6;
xlranget9= 'B70:V84';
day_9 = xlsread(filename,Sheet_time_9,xlranget9);
mn5 = mean(day_9,2);
day9N = day_9 - repmat(mn5,1,N1);
signals_t_9 = PC'*day9N;

% Day 12
Sheet_time_12 = 6;
xlranget12= 'B87:V101';
day_12 = xlsread(filename,Sheet_time_12,xlranget12);
mn6 = mean(day_12,2);
day12N = day_12 - repmat(mn6,1,N1);
signals_t_12 = PC'*day12N;

% Day 14
Sheet_time_14 = 6;
xlranget14= 'B104:V118';
day_14 = xlsread(filename,Sheet_time_14,xlranget14);
mn7 = mean(day_14,2);
day14N = day_14 - repmat(mn7,1,N1);
signals_t_14 = PC'*day14N;

% Day 16
Sheet_time_16 = 6;
xlranget16= 'B121:V135';
day_16 = xlsread(filename,Sheet_time_16,xlranget16);
mn8 = mean(day_16,2);
day16N = day_16 - repmat(mn8,1,N1);
signals_t_16 = PC'*day16N;

% Day 19
Sheet_time_19 = 6;
xlranget19= 'B138:V152';
day_19 = xlsread(filename,Sheet_time_19,xlranget19);
mn9 = mean(day_19,2);
day19N = day_19 - repmat(mn9,1,N1);
signals_t_19 = PC'*day19N;

% Day 21
Sheet_time_21 = 6;
xlranget21= 'B155:V169';
day_21 = xlsread(filename,Sheet_time_21,xlranget21);
mn10 = mean(day_21,2);
day21N = day_21 - repmat(mn10,1,N1);
signals_t_21 = PC'*day21N;

% Day 23
Sheet_time_23 = 6;
xlranget23= 'B172:V186';
day_23 = xlsread(filename,Sheet_time_23,xlranget23);
mn11 = mean(day_23,2);
day23N = day_23 - repmat(mn11,1,N1);
signals_t_23 = PC'*day23N;

% Day 26
Sheet_time_26 = 6;
xlranget26= 'B187:V203';
day_26 = xlsread(filename,Sheet_time_26,xlranget26);
mn12 = mean(day_26,2);
day26N = day_26 - repmat(mn12,1,N1);
signals_t_26 = PC'*day26N;

% Day 28
Sheet_time_28 = 6;
xlranget28= 'B155:V169';
day_28 = xlsread(filename,Sheet_time_28,xlranget21);
mn13 = mean(day_28,2);
day28N = day_28 - repmat(mn13,1,N1);
signals_t_28 = PC'*day28N;


%
%
%% Section 16.1 Interdonal Alignment Of Fingerprint Sample Age Along First Principal Alignment Axis.

spacing  = [0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1];
spacing1 = [0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2];
spacing2 = [0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3];
spacing3 = [0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4];
spacing4 = [0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5];
spacing5 = [0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6];
spacing6 = [0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7];
spacing7 = [0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8];
spacing8 = [0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9];
spacing9= [1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0];
spacing10= [1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1];
spacing11= [1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2];
spacing12= [1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3];
col1 = [1 1 0]; col2 = [0 0 0.2]; col3=[0 0.3 0];col4=[0 0.3 0.3]; col5=[0.4 0 0.4];col6=[0.2 0 0];col7=[0.1 0.1 0];
col8=[0 0 0.6];col9=[0 0.9 0];col10=[0 0.6 0.6];col11=[0.8 0 0.8];col12=[0.8 0 0];col13=[0.5 0.5 0];
figure
hold on
scatter(signals_t_28(1,:),spacing12,50,col13,'filled'); % day 28
scatter(signals_t_26(1,:),spacing11,50,col12,'filled'); % day 26
scatter(signals_t_23(1,:),spacing10,50,col11,'filled'); % day 23
 scatter(signals_t_21(1,:),spacing9,50,col10,'filled'); % day 21
  scatter(signals_t_19(1,:),spacing8,50,col9,'filled'); % day 19
  scatter(signals_t_16(1,:),spacing7,50,col8,'filled'); % day 16
  scatter(signals_t_14(1,:),spacing6,50,col7,'filled'); % day 14
  scatter(signals_t_12(1,:),spacing5,50,col6,'filled'); % day 12
   scatter(signals_t_9(1,:),spacing4,50,col5,'filled'); % day 9
   scatter(signals_t_7(1,:),spacing3,50,col4,'filled'); % day 7
   scatter(signals_t_5(1,:),spacing2,50,col3,'filled'); % day 5
   scatter(signals_t_2(1,:),spacing1,50,col2,'filled'); % day 2
    scatter(signals_t_0(1,:),spacing,50,col1,'filled'); % day 0
hold off
set(gca,'YTick',[],'XTick',[]);
title('Alignment of Aged Fingerprint Data with respect to First Principal Component Axis');
xlabel('PC1');
legend('day 28','day 26','day 23','day 21','day 19','day 16','day 14','day 12','day 9','day 7','day 5','day 2','day 0');
%
%
%% Section 16.2 Intradonal Alignment against PC1.
% CB003
% Day 0
Sheet_CB3_0 = 2;
xlrangeCB3_0= 'B2:D16';
cb3_0 = xlsread(filename,Sheet_CB3_0,xlrangeCB3_0);
[M2,N2] = size(cb3_0); mncb31 = mean(cb3_0,2);
cb3_0N = cb3_0 - repmat(mn,1,N2);
signals_cb3_0 = PC'*cb3_0N;
% Day 2
Sheet_cb3_2 = 2;
xlrangeCB3_2= 'E2:G16';
cb3_2 = xlsread(filename,Sheet_cb3_2,xlrangeCB3_2);
mncb3_2 = mean(cb3_2,2);
cb3_2N = cb3_2 - repmat(mncb3_2,1,N2);
signals_cb3_2 = PC'*cb3_2N;
% Day 5
Sheet_cb3_5 = 2;
xlrangeCB3_5= 'H2:J16';
cb3_5 = xlsread(filename,Sheet_cb3_5,xlrangeCB3_5);
mncb3_3 = mean(cb3_5,2);
cb3_5N = cb3_5 - repmat(mncb3_3,1,N2);
signals_cb3_5 = PC'*cb3_5N;
% Day 7
Sheet_cb3_7 = 2;
xlrangeCB_7= 'K2:M16';
cb3_7 = xlsread(filename,Sheet_cb3_7,xlrangeCB_7);
mncb4 = mean(cb3_7,2);
cb3_7N = cb3_7 - repmat(mncb4,1,N2);
signals_cb3_7 = PC'*cb3_7N;
% Day 9
Sheet_cb3_9 = 2;
xlrangeCB_9= 'N2:P16';
cb3_9 = xlsread(filename,Sheet_cb3_9,xlrangeCB_9);
mncb5 = mean(cb3_9,2);
cb3_9N = cb3_9 - repmat(mncb5,1,N2);
signals_cb3_9 = PC'*cb3_9N;
% Day 12
Sheet_cb3_12 = 2;
xlrangeCB12= 'Q2:S16';
cb3_12 = xlsread(filename,Sheet_cb3_12,xlrangeCB12);
mncb6 = mean(cb3_12,2);
cb3_12N = cb3_12 - repmat(mncb6,1,N2);
signals_cb3_12 = PC'*cb3_12N;
% Day 14
Sheet_CB3_14 = 2;
xlrangeCB14= 'T2:V16';
cb3_14 = xlsread(filename,Sheet_CB3_14,xlrangeCB14);
mncb7 = mean(cb3_14,2);
cb3_14N = cb3_14 - repmat(mncb7,1,N2);
signals_cb3_14 = PC'*cb3_14N;
% Day 16
Sheet_CB3_16 = 2;
xlrangeCB16= 'W2:Y16';
cb3_16 = xlsread(filename,Sheet_CB3_16,xlrangeCB16);
mncb8 = mean(cb3_16,2);
cb3_16N = cb3_16 - repmat(mncb8,1,N2);
signals_cb3_16 = PC'*cb3_16N;
% Day 19
Sheet_CB3_19 = 2;
xlrangeCB19= 'Z2:AB16';
cb3_19 = xlsread(filename,Sheet_CB3_19,xlrangeCB19);
mncb9 = mean(cb3_19,2);
cb3_19N = cb3_19 - repmat(mncb9,1,N2);
signals_cb3_19 = PC'*cb3_19N;
% Day 21
Sheet_CB3_21 = 2;
xlrangeCB21= 'AC2:AE16';
cb3_21 = xlsread(filename,Sheet_CB3_21,xlrangeCB21);
mncb10 = mean(cb3_21,2);
cb3_21N = cb3_21 - repmat(mncb10,1,N2);
signals_cb3_21 = PC'*cb3_21N;
% Day 23
Sheet_CB3_23 = 2;
xlrangeCB23= 'AF2:AH16';
cb3_23 = xlsread(filename,Sheet_CB3_23,xlrangeCB23);
mncb11 = mean(cb3_23,2);
cb3_23N = cb3_23 - repmat(mncb11,1,N2);
signals_cb3_23 = PC'*cb3_23N;
% Day 26
Sheet_CB3_26 = 2;
xlrangeCB26= 'AI2:AK16';
cb3_26 = xlsread(filename,Sheet_CB3_26,xlrangeCB26);
mncb13 = mean(cb3_26,2);
cb3_26N = cb3_26 - repmat(mncb13,1,N2);
signals_cb3_26 = PC'*cb3_26N;
% Day 28
Sheet_CB3_28 = 2;
xlrangeCB28= 'AL2:AN16';
cb3_28 = xlsread(filename,Sheet_CB3_28,xlrangeCB28);
mncb14 = mean(cb3_28,2);
cb3_28N = cb3_28 - repmat(mncb14,1,N2);
signals_cb3_28 = PC'*cb3_28N;
%
%
%% Section 16.3.
%Intraspecific CB003 PC1 Alignment
spacing  = [0.1 0.1 0.1 ];
spacing1 = [0.2 0.2 0.2 ];
spacing2 = [0.3 0.3 0.3 ];
spacing3 = [0.4 0.4 0.4 ];
spacing4 = [0.5 0.5 0.5 ];
spacing5 = [0.6 0.6 0.6 ];
spacing6 = [0.7 0.7 0.7 ];
spacing7 = [0.8 0.8 0.8 ];
spacing8 = [0.9 0.9 0.9 ];
spacing9= [1.0 1.0 1.0 ];
spacing10= [1.1 1.1 1.1 ];
spacing11= [1.2 1.2 1.2 ];
spacing12= [1.3 1.3 1.3 ];
col1 = [1 1 0]; col2 = [0 0 0.2]; col3=[0 0.3 0];col4=[0 0.3 0.3]; col5=[0.4 0 0.4];col6=[0.2 0 0];col7=[0.1 0.1 0];
col8=[0 0 0.6];col9=[0 0.9 0];col10=[0 0.6 0.6];col11=[0.8 0 0.8];col12=[0.8 0 0];col13=[0.5 0.5 0];
figure
hold on
scatter(signals_cb3_28(1,:),spacing12,50,col13,'filled'); % day 28
scatter(signals_cb3_26(1,:),spacing11,50,col12,'filled'); % day 26
scatter(signals_cb3_23(1,:),spacing10,50,col11,'filled'); % day 23
 scatter(signals_cb3_21(1,:),spacing9,50,col10,'filled'); % day 21
  scatter(signals_cb3_19(1,:),spacing8,50,col9,'filled'); % day 19
  scatter(signals_cb3_16(1,:),spacing7,50,col8,'filled'); % day 16
  scatter(signals_cb3_14(1,:),spacing6,50,col7,'filled'); % day 14
  scatter(signals_cb3_12(1,:),spacing5,50,col6,'filled'); % day 12
   scatter(signals_cb3_9(1,:),spacing4,50,col5,'filled'); % day 9
   scatter(signals_cb3_7(1,:),spacing3,50,col4,'filled'); % day 7
   scatter(signals_cb3_5(1,:),spacing2,50,col3,'filled'); % day 5
   scatter(signals_cb3_2(1,:),spacing1,50,col2,'filled'); % day 2
    scatter(signals_cb3_0(1,:),spacing,50,col1,'filled'); % day 0
hold off
%
%
%% Section 16.31 Donor CB135 PC1 Alignment.
% CB135
% Day 0
Sheet_CB135_0 = 7;
xlrangeCB3_0= 'B2:D16';
cb3_0 = xlsread(filename,Sheet_CB3_0,xlrangeCB3_0);
[M2,N2] = size(cb3_0); mncb31 = mean(cb3_0,2);
cb3_0N = cb3_0 - repmat(mn,1,N2);
signals_cb3_0 = PC'*cb3_0N;
% Day 2
Sheet_cb3_2 = 2;
xlrangeCB3_2= 'E2:G16';
cb3_2 = xlsread(filename,Sheet_cb3_2,xlrangeCB3_2);
mncb3_2 = mean(cb3_2,2);
cb3_2N = cb3_2 - repmat(mncb3_2,1,N2);
signals_cb3_2 = PC'*cb3_2N;
% Day 5
Sheet_cb3_5 = 7;
xlrangeCB3_5= 'H2:J16';
cb3_5 = xlsread(filename,Sheet_cb3_5,xlrangeCB3_5);
mncb3_3 = mean(cb3_5,2);
cb3_5N = cb3_5 - repmat(mncb3_3,1,N2);
signals_cb3_5 = PC'*cb3_5N;
% Day 7
Sheet_cb3_7 = 7;
xlrangeCB_7= 'K2:M16';
cb3_7 = xlsread(filename,Sheet_cb3_7,xlrangeCB_7);
mncb4 = mean(cb3_7,2);
cb3_7N = cb3_7 - repmat(mncb4,1,N2);
signals_cb3_7 = PC'*cb3_7N;
% Day 9
Sheet_cb3_9 = 7;
xlrangeCB_9= 'N2:P16';
cb3_9 = xlsread(filename,Sheet_cb3_9,xlrangeCB_9);
mncb5 = mean(cb3_9,2);
cb3_9N = cb3_9 - repmat(mncb5,1,N2);
signals_cb3_9 = PC'*cb3_9N;
% Day 12
Sheet_cb3_12 = 7;
xlrangeCB12= 'Q2:S16';
cb3_12 = xlsread(filename,Sheet_cb3_12,xlrangeCB12);
mncb6 = mean(cb3_12,2);
cb3_12N = cb3_12 - repmat(mncb6,1,N2);
signals_cb3_12 = PC'*cb3_12N;
% Day 14
Sheet_CB3_14 = 7;
xlrangeCB14= 'T2:V16';
cb3_14 = xlsread(filename,Sheet_CB3_14,xlrangeCB14);
mncb7 = mean(cb3_14,2);
cb3_14N = cb3_14 - repmat(mncb7,1,N2);
signals_cb3_14 = PC'*cb3_14N;
% Day 16
Sheet_CB3_16 = 7;
xlrangeCB16= 'W2:Y16';
cb3_16 = xlsread(filename,Sheet_CB3_16,xlrangeCB16);
mncb8 = mean(cb3_16,2);
cb3_16N = cb3_16 - repmat(mncb8,1,N2);
signals_cb3_16 = PC'*cb3_16N;
% Day 19
Sheet_CB3_19 = 7;
xlrangeCB19= 'Z2:AB16';
cb3_19 = xlsread(filename,Sheet_CB3_19,xlrangeCB19);
mncb9 = mean(cb3_19,2);
cb3_19N = cb3_19 - repmat(mncb9,1,N2);
signals_cb3_19 = PC'*cb3_19N;
% Day 21
Sheet_CB3_21 = 7;
xlrangeCB21= 'AC2:AE16';
cb3_21 = xlsread(filename,Sheet_CB3_21,xlrangeCB21);
mncb10 = mean(cb3_21,2);
cb3_21N = cb3_21 - repmat(mncb10,1,N2);
signals_cb3_21 = PC'*cb3_21N;
% Day 23
Sheet_CB3_23 = 7;
xlrangeCB23= 'AF2:AH16';
cb3_23 = xlsread(filename,Sheet_CB3_23,xlrangeCB23);
mncb11 = mean(cb3_23,2);
cb3_23N = cb3_23 - repmat(mncb11,1,N2);
signals_cb3_23 = PC'*cb3_23N;
% Day 26
Sheet_CB3_26 = 7;
xlrangeCB26= 'AI2:AK16';
cb3_26 = xlsread(filename,Sheet_CB3_26,xlrangeCB26);
mncb13 = mean(cb3_26,2);
cb3_26N = cb3_26 - repmat(mncb13,1,N2);
signals_cb3_26 = PC'*cb3_26N;
% Day 28
Sheet_CB3_28 = 7;
xlrangeCB28= 'AL2:AN16';
cb3_28 = xlsread(filename,Sheet_CB3_28,xlrangeCB28);
mncb14 = mean(cb3_28,2);
cb3_28N = cb3_28 - repmat(mncb14,1,N2);
signals_cb3_28 = PC'*cb3_28N;
spacing  = [0.1 0.1 0.1 ];
spacing1 = [0.2 0.2 0.2 ];
spacing2 = [0.3 0.3 0.3 ];
spacing3 = [0.4 0.4 0.4 ];
spacing4 = [0.5 0.5 0.5 ];
spacing5 = [0.6 0.6 0.6 ];
spacing6 = [0.7 0.7 0.7 ];
spacing7 = [0.8 0.8 0.8 ];
spacing8 = [0.9 0.9 0.9 ];
spacing9= [1.0 1.0 1.0 ];
spacing10= [1.1 1.1 1.1 ];
spacing11= [1.2 1.2 1.2 ];
spacing12= [1.3 1.3 1.3 ];
col1 = [1 1 0]; col2 = [0 0 0.2]; col3=[0 0.3 0];col4=[0 0.3 0.3]; col5=[0.4 0 0.4];col6=[0.2 0 0];col7=[0.1 0.1 0];
col8=[0 0 0.6];col9=[0 0.9 0];col10=[0 0.6 0.6];col11=[0.8 0 0.8];col12=[0.8 0 0];col13=[0.5 0.5 0];
figure
hold on
scatter(signals_cb3_28(1,:),spacing12,50,col13,'filled'); % day 28
scatter(signals_cb3_26(1,:),spacing11,50,col12,'filled'); % day 26
scatter(signals_cb3_23(1,:),spacing10,50,col11,'filled'); % day 23
 scatter(signals_cb3_21(1,:),spacing9,50,col10,'filled'); % day 21
  scatter(signals_cb3_19(1,:),spacing8,50,col9,'filled'); % day 19
  scatter(signals_cb3_16(1,:),spacing7,50,col8,'filled'); % day 16
  scatter(signals_cb3_14(1,:),spacing6,50,col7,'filled'); % day 14
  scatter(signals_cb3_12(1,:),spacing5,50,col6,'filled'); % day 12
   scatter(signals_cb3_9(1,:),spacing4,50,col5,'filled'); % day 9
   scatter(signals_cb3_7(1,:),spacing3,50,col4,'filled'); % day 7
   scatter(signals_cb3_5(1,:),spacing2,50,col3,'filled'); % day 5
   scatter(signals_cb3_2(1,:),spacing1,50,col2,'filled'); % day 2
    scatter(signals_cb3_0(1,:),spacing,50,col1,'filled'); % day 0
hold off
%
%
%% Section 17. Age Curves Of Major Composites Found In Principal Components For Each Donor.
% Donor CB003
t = [ 0 2 5 7 9 12 14 16 19 21 23 26 28];
xlrange3 ='B21:N21'; %sq
xlrange4 ='B22:N22'; %palm
xlrange5 ='B23:N23'; %hexa
agecurvCB3SQ= xlsread(filename,sheet,xlrange3);
agecurvCB3PM= xlsread(filename,sheet,xlrange4);
agecurvCB3HX= xlsread(filename,sheet,xlrange5);
figure
a=agecurvCB3SQ;
b=agecurvCB3PM;
c=agecurvCB3HX;
e =std(a)*ones(size(t));
e1=std(b)*ones(size(t));
e2=std(c)*ones(size(t));
hold on
a1 = plot(t,a,'r');
a2 = plot(t,b,'b');
a3 = plot(t,c,'g');
errorbar(t,a,e,'r');
errorbar(t,b,e1,'b');
errorbar(t,c,e2,'g');
hold off
legend([a1 a2 a3],'Squalene','Palmitic acid','Hexadecenoic acid');
title('Degradation Principle Composites  Against Time For CB003 Donor');
xlabel('Time (days)');
ylabel('Normalised Chromatogram Values');
% Donor CA006
xlrange6 ='B26:N26'; %hexa
xlrange7 ='B27:N27'; %palm
xlrange8 ='B28:N28'; %sq
agecurvCA6HX= xlsread(filename,sheet,xlrange6);
agecurvCA6PM= xlsread(filename,sheet,xlrange7);
agecurvCA6SQ= xlsread(filename,sheet,xlrange8);
figure
aa=agecurvCA6SQ;
bb=agecurvCA6PM;
cc=agecurvCA6HX;
ee =std(aa)*ones(size(t));
ee1=std(bb)*ones(size(t));
ee2=std(cc)*ones(size(t));
hold on
aa1 = plot(t,aa,'r');
aa2 = plot(t,bb,'b');
aa3 = plot(t,cc,'g');
errorbar(t,aa,ee,'r');
errorbar(t,bb,ee1,'b');
errorbar(t,cc,ee2,'g');
hold off
legend([aa1 aa2 aa3],'Squalene','Palmitic acid','Hexadecenoic acid');
title('Degradation Principle Composites  Against Time For CA006 Donor');
xlabel('Time (days)');
ylabel('Normalised Chromatogram Values');
% CB033
xlrange9 ='B31:N31'; %hexa
xlrange10 ='B32:N32'; %palm
xlrange11 ='B33:N33'; %sq
agecurvCB33HX= xlsread(filename,sheet,xlrange9);
agecurvCB33PM= xlsread(filename,sheet,xlrange10);
agecurvCB33SQ= xlsread(filename,sheet,xlrange11);
figure
aaa=agecurvCB33SQ;
bbb=agecurvCB33PM;
ccc=agecurvCB33HX;
eee =std(aaa)*ones(size(t));
eee1=std(bbb)*ones(size(t));
eee2=std(ccc)*ones(size(t));
hold on
aaa1 = plot(t,aaa,'r');
aaa2 = plot(t,bbb,'b');
aaa3 = plot(t,ccc,'g');
errorbar(t,aaa,eee,'r');
errorbar(t,bbb,eee1,'b');
errorbar(t,ccc,eee2,'g');
hold off
legend([aaa1 aaa2 aaa3],'Squalene','Palmitic acid','Hexadecenoic acid');
title('Degradation Principle Composites  Against Time For CB033 Donor');
xlabel('Time (days)');
ylabel('Normalised Chromatogram Values');
%DA080
xlrange12 ='B36:N36'; %hexa
xlrange13 ='B37:N37'; %palm
xlrange14 ='B38:N38'; %sq
agecurvDA80HX= xlsread(filename,sheet,xlrange12);
agecurvDA80PM= xlsread(filename,sheet,xlrange13);
agecurvDA80SQ= xlsread(filename,sheet,xlrange14);
figure
aaaa=agecurvDA80SQ;
bbbb=agecurvDA80PM;
cccc=agecurvDA80HX;
eeee =std(aaaa)*ones(size(t));
eeee1=std(bbbb)*ones(size(t));
eeee2=std(cccc)*ones(size(t));
hold on
aaaa1 = plot(t,aaaa,'r');
aaaa2 = plot(t,bbbb,'b');
aaaa3 = plot(t,cccc,'g');
errorbar(t,aaaa,eeee,'r');
errorbar(t,bbbb,eeee1,'b');
errorbar(t,cccc,eeee2,'g');
hold off
legend([aaaa1 aaaa2 aaaa3],'Squalene','Palmitic acid','Hexadecenoic acid');
title('Degradation Principle Composites  Against Time For DA080 Donor');
xlabel('Time (days)');
ylabel('Normalised Chromatogram Values');
%
%
% END OF FILE
↑ View description of PCA

Squalene Epoxide Model MATLAB Code


The figures shown in the squalene epoxide and lanosterol synthase model were created using MATLAB. Before using MATLAB the original system of equations was non-dimensionalised to the system:

$$ \begin{eqnarray*} \frac{dLS}{d\tau}&=&PC-\lambda LS \cdot SE,\\ \frac{dSE}{d\tau}&=&PC-\lambda LS \cdot SE,\\ \frac{PC}{d\tau}&=&\lambda LS \cdot SE-PC-\gamma PC,\\ \frac{dLa}{d\tau}&=&\gamma PC. \end{eqnarray*} $$

The initial conditions were also non-dimensionalised to become:

$$ \begin{eqnarray*} LS(0)&=&v_{0},\\ SE(0)&=&1,\\ PC(0)&=&0,\\ La(0)&=&0. \end{eqnarray*} $$

Two files were written to perform sensitivity analysis; one to set the function (squalene.m) and one to solve the function and plot the results in Figure 6 (run_squalene.m). Both files are shown below, where the green text is comments to aid in understanding of the scripts.



  MATLAB code from squalene.m file
% File to solve the system of ODEs describing lanosterol synthase and squalene epoxide binding.
% The vector u has 4 dimensions;
% u(1) = Lanosterol synthase (LS) concentration, {non-dimensionalised}
% u(2) = Squalene epoxide (SE) concentration, {"}
% u(3) = Protosterol cation (PC) concentration (1st Intermediate), {"}
% u(4) = Lanosterol (La) concentration. {"}
% t is the time that the simulation is run over.
% lambda is the 1st binding parameter ((k1/k2)SE(0)).
% gamma is the 2nd binding parameter (k3/k2).
function f = squalene(t,u,lambda,gamma);
% Then set f as the RHS of the system of ODEs.
f = [u(3)-lambda.*u(1)*u(2);
    u(3)-lambda.*u(1)*u(2);
    lambda.*u(1)*u(2)-u(3)-gamma.*u(3);
    gamma.*u(3)];
end
% Then end the function.
% This function can then be solved using ode23 in the file run_squalene.m  by using the @squalene command.
% END OF FILE.


MATLAB code for run_squalene.m file.
% File to solve the non-dimensionalised system of ODEs representing the binding of squalene epoxide (SE) and lanosterol synthase (LS) to form lanosterol (La).
%
% Set the final time of the simulation, set at 30 seconds.
T = 30;
% Set initial concentration of ratio (LS/SE) as the expected value.
u0 = 2.561;
% Parameter a is how many values of each parameter are used in the sensitivity analysis.
a = 100;

% Set lambda1 as the range of values for parameter lambda, where the maximum value is twice the expected.
lambda1 = linspace(0,(0.64061499*2),a);
% Set gamma1 as the range of values for parameter gamma, where the maximum value is twice the expected.
gamma1 = linspace(0,(1.000223733*2),a);
% Set Store as an empty matrix to store the values of lanosterol concentrations for each range of values of lambda1 and gamma1.
Store = zeros(a,a);
% Set a for loop that will solve the system of ODEs from the squalene.m file using the ode23 solver, for each value of lambda1, gamma1.

% The resulting values for the lanosterol concentration are stored in the Store matrix.
for i=1:a
    for j=1:a
[t,u]=ode23(@squalene,[0 T],[u0 1 0 0],[],lambda1(a+1-i),gamma1(j));
 Store(i,j) = u(end,4);

    end
end
% Call up a blank figure, so that no other figures are overwritten.
figure(1)
% Plot a colourplot of Store, that is plot the lanosterol concentration against lambda1 and gamma1.

imagesc(Store)
% Set the colormap as default colour choice, as this is easiest to see.
colormap default
% Remove the values on the x and y axis by using the set command.
set(gca,'YTick',[],'XTick',[]);
% Add a colorbar with user defined axis labels (Tick labels) and label,
% 'Complex Concentration'.
c=colorbar('Ticks',[0,0.99],'TickLabels',{'None','High'},'FontSize',15,'FontWeight','bold');
c.Label.String = 'Complex Concentration';
% Add labels to the x and y axis for clarity on the plot.
xlabel('\fontsize{12} \bf Increasing \lambda');
ylabel('\fontsize{12} \bf Increasing \gamma');
%
%
%% Section 2: This section is used to plot only lambda against lanosterol concentration over time.
% Define store1 as an empty matrix to hold values of LS, SE, PC (1st Intermediate) and La, for each value of lambda1.
store1 = zeros(5000,5,a); % 1st is time, 2:5 are u.
% Set a for loop that will solve the system of ODEs from the squalene.m file using the ode23 solver, for each value of lambda1, with the expected value of gamma1 used.
% The resulting values for LS, SE, PC and the lanosterol concentration are stored in the store1 matrix.
for i=1:a

    [t,u]=ode23(@squalene,[0 T],[2.561 1 0 0],[],lambda1(i),1.000223733);
    store1(end-size(t,1)+1:end,1,i) = t;
    store1(end-size(t,1)+1:end,2:5,i) = u;

end
% Call up a blank figure, so that no other figures are overwritten.
figure(2)
% Plot the values of lambda1 against the corresponding values of lanosterol concentration over time.

 plot(lambda1,squeeze(store1(end,5,:)),'LineWidth',2);
 % Add labels to the x and y axis for clarity on the plot.
 xlabel('\bf \fontsize{12}Increasing \lambda');
 ylabel('\bf \fontsize{12} Lanosterol Concentration');
 % Set the axis to tight so that the axis is not too large for the data.
 axis tight
 %
 %
%% Section 3: This section is used to plot only gamma against lanosterol concentration over time.
% Define store2 as an empty matrix to hold values of LS, SE, PC and La, for each value of gamma1.
store2 = zeros(a,5,a); % 1st is time, 2:4 are u.
% Set a for loop that will solve the system of ODEs from the squalene.m file using the ode23 solver, for each value of gamma1, with the expected value of lambda1 used.
% The resulting values for LS, SE, PC and the lanosterol concentration are stored in the store2 matrix.
for i=1:a

    [t,u]=ode23(@squalene,[0 T],[2.561 1 0 0],[],0.64061499,gamma1(i));
    store2(end-size(t,1)+1:end,1,i) = t;
    store2(end-size(t,1)+1:end,2:5,i) = u;

end
% Call up a blank figure, so that no other figures are overwritten.
figure(3)
% Plot the values of gamma1 against the corresponding values of lanosterol concentration over time.
 plot(gamma1,squeeze(store2(end,5,:)),'LineWidth',2);
% Add labels to the x and y axis for clarity on the plot.
  xlabel('\bf Increasing \gamma');
 ylabel('\bf Lanosterol Concentration');
% Set the axis to tight so that the axis is not too large for the data.
 axis tight
 %
 %
%% Section 4: This section is used to plot only v0, the ratio of (LS(0)/SE(0)) against lanosterol concentration over time.
% Define store3 as an empty matrix to hold values of LS,SE,PC and La, for each value of v0.
store3= zeros(a,5,a);
% Set v0 as the range of values for v0 with the maximum as twice the expected value.
v0=linspace(0,(2.561*2),a);
% Set a for loop that will solve the system of ODEs from the squalene.m file using the ode23 solver, for each value of v0, with the expected value of lambda and gamma used.
% The resulting values for LS, SE, PC and the lanosterol concentration are stored in the store3 matrix.
for i=1:a
    [t,u]= ode23(@squalene,[0 T],[v0(i) 1 0 0],[],0.64061499,1.00223733);
    store3(end-size(t,1)+1:end,1,i) = t;
    store3(end-size(t,1)+1:end,2:5,i) = u;
end
% Call up a new figure, so that no figures are overwritten.
figure(4)
% Plot the values of v0 against the corresponding values of lanosterol concentration over time.
plot(v0,squeeze(store3(end,5,:)),'LineWidth',2);
% Set the axis to tight so that the axis is not too large for the data.
axis tight;
% Add labels to the x and y axis for clarity on the plot.
xlabel('\bf \fontsize{12} Increasing v_{0}');
ylabel('\bf \fontsize{12} Concentration of Lanosterol formed');
%
% END OF FILE.
↑ View description of model

To see the MATLAB code for the FluID section of the project or the Chromate Biosensor section of the project use the following buttons.


Appendix 3: Chromate Biosensor Appendix 1: FluID